Auto focusing process for synthetic antenna sonars

ABSTRACT

The invention relates to autofocusing processes for synthetic antenna sonars. 
     It consists in using at least two frequencies having different phase centers and the positions of which vary along the physical receiving antenna from one recurrence to the next. In one embodiment, three distinct frequencies are used, one for the image and the other two for the autofocusing. In another embodiment, two distinct frequencies are used, which serve alternately for the autofocusing and for the image. In another embodiment at least three distinct frequencies are used, all of which serve in the autofocusing and the formation of the image by aperture synthesis and the transmission phase centers of which, distributed at a constant spacing along the physical receiving antenna, are displaced from one recurrence to the next according to a cyclic permutation.

The present invention relates to synthetic antenna sonars in which thephysical antenna is formed by a linear array of transducers. All thetransducers are active in receive mode whereas only some of them areused for transmission.

To form the channels of such a synthetic antenna, the K×N signalsdelivered by the N transducers during K successive recurrences arecombined linearly. To do this, it is necessary to know the geometry ofthe synthetic antenna, that is to say the position of the phase centresof the transmitting and receiving transducers, for the duration of the Krecurrences in a plane Oxy where Ox is the beam axis towards the bottom(whose inclination in the elevation plane varies within the recurrencelike the elevation of the bottom) and Oy is the axis perpendicular to Oxwhich is closest to the mean path of the platform. The deviations of thesynthetic antenna with respect to the plane Oxy are small enough to beneglected in most practical cases.

Means are also available which are accurate enough for measuring thedisplacement of the support of the transducers along Oy, in respect ofwhich direction less accuracy is needed than in respect of Ox. Thus, theproblem of knowing the geometry of the synthetic antenna in the planeOxy is reduced to that of knowing its geometry along the beam axis Ox.

To solve this problem the Westinghouse company has proposed applying theprinciple of equivalent phase centres in "Synthetic aperture beamformingwith automatic phase compensation for high frequency sonars", R. W.Sheriff, AUV 92 1!. To do this, the deviation is determined between thesum of the abscissae x_(k) of the transmission phase centre atrecurrence k and x_(n),k of the phase centre of receiving sensor n atrecurrence k, and the sum of the abscissae x_(k+1) of the transmissionphase centre at recurrence k+1 and of receiving sensor n' at recurrencek+1 by measuring the intercorrelation delay of the two signals fromsensors (n,k) and (n',k+1) chosen such that:

    Y.sub.k +Y.sub.n,k =Y.sub.k+1 +Y.sub.n',k+1                ( 1)

which is the condition of phase centre equivalence corresponding to amaximum correlation for the signals received on sensor n at recurrence kand sensor n' at recurrence k+1.

In the document 1! an array of two transducers is considered, the firstof which is used in transmit and receive mode, and the second in receivemode only. The displacement in the Oy direction between two successiverecurrences being equal to half the distance between the two sensors,relation (1) is satisfied by n=2 and n'=1. As represented in FIG. 1,this can be generalized to an array of N sensors and to a displacementδy of less than half the length of the array for every Y_(n),k such that

    Y.sub.n,k -2.δy≧Y.sub.1,k                     ( 2)

Spatial interpolation over the signals of recurrence k+1 can be used todetermine a sensor signal corresponding to a position y_(n'),k+1 of itsphase centre over Oy such that we have (1) (since y_(k+1) =y_(k) +δy andy_(n'),k+1 =y_(n'),k +δy, (1) is equivalent to y_(n),k =y_(n),k +2.δy),and to then estimate the intercorrelation delay between the interpolatedsensor, (n',k+1) and the sensor (n,k), which will be denoted τ_(n'),n,k.The spatial interpolation leads us to consider fractional indices n'. Wehave τ_(n'),n,k =τ_(n'),n,k,x +τ_(n'),n,k,y where τ_(n'),n,k,x dependson the abscissae x_(k), x_(k+1), x_(n),k, x_(n'),k+1 which it is desiredto estimate and τ_(n'),n,k,y depends on the ordinates y_(k), y_(k+1),y_(n),k and y_(n'),k+1. The ordinates being known, τ_(n'),n,k,y isknown. The measurement of τ_(n'),n,k,x =τ_(n'),n,k -τ_(n'),n,k,y isdeduced from the measurement of τ_(n'),n,k.

We then obtain a set of pairs of transmission/reception phase centres((n,k), (n',k+1)), an estimate of the deviation of the abscissae ofwhich is given by:

    (X.sub.k+1 +X.sub.n',k+1)-(X.sub.k +X.sub.n,k)=-C.τ.sub.n',n,k,x( 3)

The ordinates of the transmission phase centres y_(k) and y_(k+1), andreception phase centres y_(n),k and y_(n'),k+1 are given by measuringthe displacement in the direction Oy obtained by the measurement meansmentioned above.

It is therefore possible to estimate the shape of the synthetic antennagradually (from recurrence to recurrence), this leading to theconsideration that x_(k) +x_(n),k is known, (3) then giving x_(k+1)+x_(n'),k+1. The array being linear, we need only know x_(k+1)+x_(n'),k+1 for at least two values of n' in order to calculate bylinear regression the abscissae x_(k+1) +x_(n),k+1 of the N actualtransmission/reception phase centres (that is to say those which are notspatially interpolated, n an integer) for recurrence k+1. A measure ofthe rotation of the antenna may possibly also be taken into account inthe estimation of the x_(k+1) +x_(n),k values.

The simplest way of carrying out the autofocusing processing consists incompensating for the deviations of the synthetic antenna with respect toOy by applying delays defined by the following formula to the signalsfrom the sensors, c being the speed of sound in water: ##EQU1##

Channel formation is then carried out as for an antenna with the samey_(k) and y_(n),k values, but whose x_(k) and x_(n),k values are allzero.

When the deviations in the direction Ox along the antenna are too large,this simple correction can no longer be used, the focusing delays thendepending in a non-separable manner on the estimated deformed shape andon the point of focusing.

This method is all the more accurate the larger the number of sensorswhich can be paired up between two successive recurrences k and k+1according to relation (1). The constraint (2) produces a limitation onthis. For a sufficient number of sensors, this relation (2) implies thatthe number of sensors for recurrence k which can be used to estimate thetransverse displacement of the antenna between recurrences k and k+1 isgiven by: ##EQU2##

Hence, it may be seen that in order for there to be a significantproportion of usable sensors, the interrecurrence displacement must bemarkedly less than L/2. Moreover, L/2 is the maximum value of theinterrecurrence displacement beyond which spatial under-sampling of thesynthetic antenna occurs, impairing its performance as is explained inthe article "Detection and Imaging Performance of a Synthetic ApertureSonar", D. Billon, F. Le Clerc, L. Hue, OCEANS 93, 2!. In practice, thislimitation is constraining: if L=3 m and the range R_(max) of the sonaris equal to 500 m, the maximum speed is V=(L/2)/(2R_(max) /c)=4.5 knots.A further lowering of the speed limit would therefore be difficult toaccept.

In order to implement the autofocusing method described earlier withoutlowering the speed limit, it is proposed to displace the phase centrefor transmission k+1 electronically in the direction opposite to thephysical displacement of the antenna, with respect to the phase centrefor transmission k. The constraint (2) then becomes:

    y.sub.n,k ≧y.sub.1,k +2δy-e                   (6)

where e is the rearwards electronic displacement of the transmissionphase centre for recurrence k+1 with respect to recurrence k, that is tosay y_(k+1) =y_(k) +δy-e. For e=2.δy all of the sensors of the antennacan be used for the autofocusing since the constraint (6) which can thenbe written y_(n),k ≧y₁,k is satisfied for every n.

In the general case the number of sensors which can be used for theautofocusing is: ##EQU3##

This process of electronically displacing transmission in the directionopposite to the advancing of the platform so as to afford a strongcorrelation in the signals of two successive recurrences is known in thefield of radar, for applications other than synthetic antennaautofocusing, where the corresponding type of antenna is called DPCA(Displaced Phase Centre Antenna).

The invention involves applying such a process for autofocusing thesynthetic antennas of a sonar.

According to a first embodiment, two different frequencies f₁ and f₂ areused to perform the autofocusing, and a third different frequency f₀ toform the image.

According to another characteristic of this first embodiment, thefrequencies f₁ and f₂ are transmitted alternately at the ends of theantenna, and the frequency f₀ at a fixed point thereof, for example thecentre.

According to a second embodiment, two different frequencies f₁ and f₂are used, the transmission phase centres of these frequencies aredisplaced. in opposite directions over K successive recurrences and thenthe directions of displacement are reversed, the frequency whose phasecentre is displaced towards the front of the antenna is used to form asynthetic antenna over these K recurrences, and the other frequency isused to perform the autofocusing.

According to another characteristic of this second embodiment, thevalues K=2 and K=3 correspond to two preferred cases of the secondembodiment.

According to a third embodiment, M distinct frequencies f₁, . . . f_(M)are used, the transmission phase centres of which are distributed alongthe physical receiving antenna with a constant spacing and are displacedaccording to a cyclic permutation at each new recurrence. This cyclicpermutation displaces, by one spacing forwards, the phase centres of M-1frequencies out of the M frequencies, and by M-1 spacings rearwards thephase centre of the remaining frequency, this being the only one used toapply the principle of equivalent phase centres between the newrecurrence and the preceding recurrence so as to estimate the motionalong Ox according to the general process of the invention. The Mfrequencies are used to form the image by aperture synthesis.

Other features and advantages of the invention will emerge clearly fromthe following description, given by way of non-limiting example withregard to the appended figures which represent:

FIG. 1, an explanatory diagram of the known process of reference 1!generalized for a linear array of N sensors,

FIG. 2, an explanatory diagram of a first embodiment of the invention,

FIG. 3, an explanatory diagram of a first example of a second embodimentof the invention,

FIG. 4, an explanatory diagram of a second example of this secondembodiment; and

FIG. 5, an explanatory diagram of a third embodiment of the invention.

In a first embodiment, the process according to the invention is used toproduce a side-looking sonar operating at a relatively "thigh" speed.

This sonar operates in three frequency bands centred on f₀, f₁ and f₂.The phase centre for the transmission at f₀ is fixed, thus enabling thesonar image to be formed in this frequency band.

The frequencies f₁ and f₂ are used in accordance with the processdescribed above to estimate the geometry of the synthetic antenna. Thetransmission phase centres f₁ and f₂ are on an axis parallel to theantenna and 2.δy distant, it being possible to achieve this by usingsome of the transducers of the receiving antenna for transmission. Theallocation of f₁ and f₂ to the two phase centres is alternated fromrecurrence to recurrence. For a given pair of successive recurrences,that one of the two frequencies f₁ and f₂ which was transmitted at thefront at recurrence k and at the rear at recurrence k+1 is used toobtain the autofocusing (determination of the correction delays for thedeviations with respect to Oy or of the geometry of the antenna in Oxyas explained earlier) For the next pair, consisting of recurrences k+1and k+2, the other frequency transmitted at the front at recurrence k+1and at the point shifted backwards by 2.δy at recurrence k+2 is used,and so on.

In the more general case, it is possible to choose the location of thephase centre shifted backwards to within a transducer spacing byspatially switching the transmission circuits in a transducer arraywhich may be the same as that for reception, so that e is as close aspossible to 2.δy for δy≦L/2. In practice the highest possible speed, andhence δy close to L/2, will be sought. This case corresponds to aparticular layout in which the transmitters operating at the frequenciesf₁ and f₂ and serving in the autofocusing are located at the two ends ofthe antenna. The position of the transmitter operating at the frequencyf₀ and serving for the imaging is unimportant provided that it is fixed.In a particular layout, the centre of the antenna and the two extremetransmitters operate alternately at f₁ and f₂. This configuration inwhich transmission occurs on two frequencies alternating at the two endsof the antenna is described in U.S. Pat. No. 5,295,118 filed on 18 Feb.1993 and published on 15 Mar. 1994. However in this patent, the aim ofthis transmission device is to double the speed of the platform and thesignals received are not employed for autofocusing as is proposed in thepresent invention; this would not be possible since in this case we haveL=e=δy and relation (7) shows that the number of sensors which can beused to autofocus the antenna is zero. Furthermore, the transmissiondevices are different since in a first embodiment the invention usesthree frequencies, one sonar imaging frequency and two auxiliaryautofocusing frequencies, as represented in FIG. 2 and, in a secondembodiment, the invention uses two frequencies whose transmission phasecentres are not necessarily at the two ends of the antenna and may belocated at more than 2 points during the recurrences.

In a concrete example of this first embodiment, the following parametershave been used:

range, recurrence: R_(max) =500 m, Tr=670 ms

antenna length, speed: L=4 m, V_(max) =6 knots

frequencies: f₀ =100 kHz, f₁ =90 kHz, f₂ =80 kHz

bandwidth: B₀ =20 kHz, B₁ =10 kHz, B₂ =10 kHz

pulse duration: T₀ =T₁ =T₂ =5 ms (in "chirp" form) form

number of sensors: N=80, K=30 at the maximum range of 500 m

length of the transmission pupils: l₀ =0.1 m, l₁ =l₂ =0.4 m

aperture of the transmission diagrams: 2θ-3,0=8°, 2θ-3,1≈2θ-3,2≈2°

(the index n in θ-3,n indicates the corresponding frequency fn)

resolution along Ox: c/2B₀ =4 cm, along Oy: l₀ /2=5 cm.

Autofocusing beams which are finer than those used for the imaging areemployed because the autofocusing method works all the better the finerthe beams, whilst the resolution of the synthetic antenna is inverselyproportional to the width of the transmission beam. The threetransmission beams are azimuthally stabilized in a direction Oxperpendicular to the mean position of the antenna by means of anattitude unit, the output from which is merged with the estimate of therotation of the antenna in the plane Oxy, as provided by theautofocusing. Electronic pointing is carried out by using the twocentral transducers at f₀ and the 8 transducers at each end at f₁ andf₂. Spatial oversampling of the actual antenna facilitates the spatialinterpolation required by the autofocusing method.

In a second embodiment, the process according to the invention is usedto produce a hull sonar intended to operate at "slow" speed in order tocarry out mine hunting.

In a known manner, in order to classify an object detected by means ofits detecting sonar, the mine hunting vessel approaches the suspectobject detected at a safety distance of the order of 150 meters and usesits shadow classifying sonar to obtain an image classifying the object.To do this it rotates about the object while maintaining its safetydistance and it analyses the deformation of the acoustic shadow cast onthe bottom in this motion so as to obtain the shape of the object. Thequality of the image from the shadow is limited chiefly by the azimuthalresolution of the sonar, which is of the order of 0.1° to 0.2°, thisbeing of the same order of magnitude as the size of the objects to beclassified. The invention therefore proposes to implement syntheticantenna processing in order to improve this resolution during thecircular motion of the boat about the object, this being of greatinterest operationally. This motion can be performed at low speed, ofthe order of 2 knots along an axis parallel to the antenna. For aduration of recurrence of 250 ms, corresponding to a maximum range of180 m, the displacement is 25 cm, this leaving a span of 1 m in a 1.5 mantenna (=1.5 m-2×0.25 m) to carry out autofocusing with a transmissionwhose phase centre on the antenna is fixed. The same frequency can thenbe used to form the image and to carry out autofocusing.

The angular resolution of the synthetic antenna in a bottom regioninsonified during the K successive recurrences is ##EQU4## to becompared with the resolution of the actual antenna: ##EQU5##

In the above example (L=1.5 m, δy=0.25 m), K=4 is therefore required inorder to divide the angular resolution by two and K=7 in order to divideit by three. Although these numbers are low as compared with the exampleof the first embodiment (K=30), they are difficult to use here since,whereas the first embodiment applies chiefly to side-looking sonarsmounted on towed vehicles navigating near the bottom, the secondembodiment described below relates essentially to hull sonars whoseantenna is only a few meters below the surface where the spatio-temporalcoherence of the medium is markedly smaller than near the bottom.Consequently, for a given objective as regards the resolution of thesynthetic antenna, it is important to minimize the physical displacementof the actual antenna and the formation time for the synthetic antenna,this amounting to minimizing K. Another advantage of minimizing K isthat it simplifies the synthetic antenna autofocusing and formationprocessing operations. This is the subject of this second embodiment ofthe invention.

In this embodiment there are only two frequencies f₁ and f₂. During theK successive recurrences which serve to form the synthetic antenna, thetransmission phase centre, for example f₁, is displaced along theantenna in the direction of the motion of the antenna at each newrecurrence, whilst the transmission phase centre of the other frequency,for example f₂, is displaced in the opposite direction. The frequency f₁is used to form the synthetic antenna and the frequency f₂ to autofocusit according to the principle set out earlier. During the K-1 succeedingrecurrences the direction of the displacements of the transmission phasecentres of f₁ and f₂ is reversed and a synthetic antenna is formed atthe frequency f₂ with the last of the K previous recurrences and theseK-1 new recurrences. And so on and so forth. If T_(r) is the duration ofthe recurrence of the sonar, the period of the images formed in this wayis (K-1).T_(r).

If E is the total excursion during the K recurrences of the phase centrefor the transmission at the frequency serving to form the syntheticantenna, the angular resolution obtained is ##EQU6##

Let e₊ and e₋ be the displacements between two recurrences respectivelyof the phase centre for the transmission at the synthetic antennaformation frequency and of the phase centre for the transmission at thesynthetic antenna autofocusing frequency. The following constraint musthold:

    e.sub.+ +2δy≦L                                (11)

This expression represents the condition of correct spatial sampling ofthe synthetic antenna. The number I of sensors to which the principle ofphase centre equivalence can be applied, at the frequency whosetransmission phase centre shifts backwards, is given by expression (7)where e=e-.

In a first concrete example of this second embodiment, represented inFIG. 3, the parameters are the following:

L=1.5 m, N=100, f₁ =410 kHz, f₂ =430 kHz

B₁ =B₂ =15 kHz, T₁ =T₂ =7 ms

Length of the 2 transmission pupils=10.5 cm

Field width at 150 m and -3 dB of attenuation in the sound level=4.5 m

K=2, E=e₊ =e₋ ≦1.4 m

Image recurrence=sonar recurrence=250 ms

Resolution at 150 m and at the speed of 2 knots=0.05 m×0.18 m.

The two transducers are made up of 7 elements which are elements of thereceiving array. The spacing E of the two phase centres is slaved to thetransverse speed V with respect to the beam axis according to therelation:

    E=2V.T.sub.r                                               (12)

where T_(r) =250 ms. This variable spacing is produced by electronicallyswitching the elements of the transducers from among the 100 elements ofthe receiving array.

The two beams are pointed onto the centre of the object to be classifiedinitially through operator designation and subsequently by slaving as afunction of the measurements of the heading and speed of the boat.

In a second concrete example, represented in FIG. 4, the parameters arethe same, except for:

K=3, E=1.4 m, e₊ =e₋ =0.75 m or 0.65 m

Image recurrence=2×sonar recurrences=500 ms

Resolution at 150 m and at the speed V=2 knots=0.05 m×0.14 m.

As represented in FIG. 4, there are four transmission phase centres at±5 cm and ±0.7 m from the centre.

The invention also proposes a third embodiment, which is more complexand which applies essentially to high-speed side-looking sonars, as inthe first embodiment, compared with which it has the advantage of makingall the transmitted frequencies available for the imaging by aperturesynthesis. The desired sonar pulse is divided spectrally into M pulseswith central frequencies f₁, f₂, . . . , f_(M) and with the samebandwidth equal to the bandwidth of the desired pulse divided by M. Thetransmission phase centres are distributed along the physical receivingantenna with a constant spacing p and their allocation to the Mfrequencies is modified at each new recurrence according to a cyclicpermutation such that all the frequencies have their phase centresadvanced by one spacing, except for one whose phase centre is shiftedbackwards by M-1 spacings with respect to the direction of advance ofthe carrier. The spacing p must satisfy relation (11) with e+=p. Thenumber I of sensors to which the principle of phase centre equivalenceis applied, at the frequency whose transmission phase centre is shiftedbackwards with respect to the previous recurrence so as to estimate themotion along Ox according to the process of the invention, is given byexpression (7) where e=(M-1)p. A particular case of interest is that inwhich M and p are chosen in such a way that all the sensors can be usedto carry out autofocusing.

We then have:

    (M-1)p=2δy                                           (13)

and, in view of (11) in which we put e₊ =p, we must have ##EQU7##

This third embodiment corresponds to the example represented in FIG. 5in which the parameters are:

R_(max) =500 m, L=4 m

T_(r) =700 ms, V_(max) =5 knots (→δy=3.5 m)

M=8, p=0.5 m

f₁ =91.25 kHz, f_(m) +1=f_(m) +2.5 Hz

B₁ +B₂ = . . . =B₈ =2.5 kHz

T₁ =T₂ = . . . =T₈ =30 ms

N=80, K=30 at 500 m

l₁ =l₂ . . . l₈ +0.1 m

2θ-3.1=2θ-3.2= . . . 2θ-3.8=8°

Resolution along Ox: c/2B=4 cm

Resolution along Oy: l_(m) /2=5 cm.

I claim:
 1. Autofocusing process for synthetic antenna sonar,characterized in that at least two frequencies are used having differentphase centres and the positions of which vary along the physicalreceiving antenna from one recurrence to the next.
 2. Process accordingto claim 1, characterized in that two different frequencies f₁ and f₂are used to perform the autofocusing, and a third different frequency f₀to form the image by aperture synthesis.
 3. Process according to claim2, characterized in that the frequencies f₁ and f₂ are transmittedalternately at the ends of the antenna, and the frequency f₀ at a fixedpoint thereof.
 4. Process according to claim 1, characterized in thattwo different frequencies f₁ and f₂ are used, in that the transmissionphase centres of these frequencies are displaced in opposite directionsover K successive recurrences and in that the directions of displacementare reversed, in that the frequency whose phase centre is displacedtowards the front of the antenna is used to form a synthetic antennaover these K recurrences, and in that the other frequency is used toperform the autofocusing.
 5. Process according to claim 4, characterizedin that K=2.
 6. Process according to claim 4, characterized in that K=3.7. Process according to claim 1, characterized in that M frequencies areused, M≧3, in that their M transmission phase centres are distributed ata constant spacing along the receiving antenna, in that the one-to-onecorrespondence between the M phase centres and the M frequencies ismodified at each new recurrence according to a cyclic permutation, thephase centres of M-1 frequencies being advanced by one spacing and thatof the remaining frequency being shifted backwards by M-1 spacings, andin that each of the M frequencies serves in the autofocusing and in theaperture synthesis.